Elementary All Subjects: Arithmetic (Objectives, Calculation, Figures, Change and Data)

The answer is "mathematical activities". The 2017 objective says "through mathematical activities". "Arithmetical activities" is the term of the previous 2008 version. Language activities and hands-on activities are stressed elsewhere (for example, the General Provisions), but they are not the wording of the arithmetic objective.

The answer is "integrative and developmental" (統合的・発展的), the wording of objective (2). "Multi-faceted and multi-angled" is used in places such as the objectives of junior high school social studies and of moral education (the elementary social studies objective says "from multiple angles"). "Scientific" is typical of science. "Proactive and interactive" appears as "proactive, interactive and deep learning" in the General Provisions and the planning section, not in objective (2).

The correct option is “Grades 1-3 have 'measurement'; Grades 4-6 have 'change and relationships'”. Grades 1-3 have A Numbers and Calculations, B Figures, C Measurement and D Using Data; in Grades 4-6, area C becomes Change and Relationships. The option giving four areas to all grades lists the areas of the previous 2008 version. The option saying only Grades 1-2 have 'measurement' has the wrong boundary: Grade 3 also has "measurement". The two areas never appear in the same grade, so the option saying all grades have both is wrong.

The answer is "use 3.14". The handling of content for Grade 5 (B Figures) and Grade 6 (B Figures) says pi is 3.14. There is no rule to use 3. 22/7 is one approximation of pi, but it is not in the Course of Study. The symbol π is learned in junior high school and is not in the elementary terms and symbols.

The answer is drawing regular polygons in Grade 5. The Course of Study gives it as a case that needs exact repetition, and where changing one part lets children draw many regular polygons in the same way. Line graphs, symmetrical figures and the soroban are not given as programming examples.

The answer is "mode". Grade 6 lists mean, median, mode, dot plot, class (interval) and others. Least common multiple is in Grade 5, diagonal in Grade 4, and inequality sign in Grade 3.

The correct option is “Adding and subtracting fractions with different denominators: Grade 5” (A Numbers and Calculations). Expressions with letters a and x are Grade 6, and so is inverse proportion. Per-unit quantities such as speed are Grade 5 (C Change and Relationships).

The answer is 12. The side of the square is the least common multiple of 18 and 24, which is 72 cm. That is 72 ÷ 18 = 4 tiles one way and 72 ÷ 24 = 3 tiles the other, so 4 × 3 = 12. Six confuses this with the greatest common divisor, 6. 18 and 24 wrongly use the side lengths as the number of tiles.

The answer is 89. Dividend = divisor × quotient + remainder, so 7 × 12 + 5 = 89. 84 forgets to add the remainder, 79 subtracts it, and 96 mixes up the relationship (for example adding 12 to 7 × 12).

The answer is 360 ÷ 12 = 30. To make 0.12 a whole number, multiply by 100; multiplying 3.6 by 100 as well gives 360, and the quotient does not change. 36 ÷ 12 multiplies the dividend by only 10. 3600 ÷ 12 multiplies the dividend by 1000. 36 ÷ 120 multiplies the divisor by 1000. None of these multiply both by the same number.

The answer is 6/5. Dividing by a fraction is the same as multiplying by its reciprocal: 3/4 × 8/5 = 24/20 = 6/5. 15/32 multiplies without taking the reciprocal. 5/6 is the reciprocal of the right answer. 3/5 just uses the two numerators.

The answer is 7/12. With a common denominator of 12: 8/12 + 9/12 − 10/12 = 7/12. 0 comes from computing numerators (2 + 3 − 5) and denominators separately. 5/12 and 1/12 come from not converting the numerators correctly.

The answer is at least 3450 and less than 3550. We round at the tens digit: 3450 rounds up to 3500, 3549 rounds down to 3500, and 3550 rounds up to 3600. “At least 3400 and less than 3500” only rounds up, and “at least 3500 and less than 3600” only rounds down. “At least 3451 and at most 3550” wrongly excludes 3450 and includes 3550.

The answer is 2.36: 23 tenths is 2.3, and 6 hundredths is 0.06, so the total is 2.36. 23.6 treats 23 as the whole-number part. 2.306 puts the 6 in the thousandths place. 0.236 shifts every digit one place down.

The answer is the distributive law, in the form (a − b) × c = a × c − b × c. The commutative law swaps the order, as in a × b = b × a. The associative law changes the grouping, as in (a × b) × c = a × (b × c). The property that the quotient does not change is about division and is not used here.

The answer is 120°. The interior angles of a hexagon add up to 180 × (6 − 2) = 720°, and in a regular hexagon all six are equal, so 720 ÷ 6 = 120°. 60° is the exterior angle. 108° is one angle of a regular pentagon, and 135° of a regular octagon.

The answer is 42 cm². Area = (top base + bottom base) × height ÷ 2 = (4 + 10) × 6 ÷ 2 = 42. 84 forgets to divide by 2. 60 uses only the bottom base times the height, and 24 only the top base times the height.

The answer is 78.5 cm². Area = radius × radius × pi; the radius is 5 cm, so 5 × 5 × 3.14 = 78.5. 31.4 is the circumference (diameter × pi = 31.4 cm). 314 uses the diameter as the radius. 15.7 is half the circumference.

The answer is 250 a. 1 ha = 10,000 m² and 1 a = 100 m², so 1 ha = 100 a, and 2.5 ha = 2.5 × 100 = 250 a. 25 a assumes 1 ha = 10 a; 2500 a and 25000 a use a factor other than 100.

The answer is 3 L. The volume is 20 × 15 × 10 = 3000 cm³, and 1 L = 1000 cm³, so 3000 ÷ 1000 = 3 L. 30 L assumes 1 L = 100 cm³, 0.3 L assumes 1 L = 10,000 cm³, and 300 L assumes 1 L = 10 cm³.

The answer is the rectangle. It has two lines of symmetry, and it matches itself when turned 180° around the point where the diagonals cross. The equilateral triangle and the regular pentagon have line symmetry, but regular polygons with an odd number of sides do not have point symmetry. A parallelogram (other than a rectangle or rhombus) has point symmetry but no line symmetry.

The answer is 1 km: 4 × 25,000 = 100,000 cm = 1,000 m = 1 km. 10 km and 100 m come from errors in the number of zeros when converting cm to m or km. 2.5 km misreads 25,000 cm (the actual length for 1 cm) as 2.5 km.

The answer is 108 km. 15 minutes is 15 ÷ 60 = 0.25 hours, so 2 hours 15 minutes is 2.25 hours, and 48 × 2.25 = 108 km. 103.2 km treats it as 2.15 hours. 96 km ignores the 15 minutes, and 120 km uses 2.5 hours.

The answer is 2,400 yen. 25% off means 1 − 0.25 = 0.75 of the list price: 3,200 × 0.75 = 2,400. 800 yen is the discount itself (3,200 × 0.25). 3,175 yen misreads it as 25 yen off. 4,000 yen is the price with 25% added.

The answer is 75. Treating the whole as 3 + 5 = 8 parts, B gets 120 × 5/8 = 75 (A gets 45). 72 is 120 × 3/5, which confuses the ratio value with a share. 45 is A's share. 80 is 120 × 2/3, which has nothing to do with the ratio.

The correct option is the length and width of a rectangle with an area of 24 cm². Length × width = 24 is constant, so when the length doubles the width halves: inverse proportion. Ribbon length and price (price = 80 × length) and a square's side and perimeter (perimeter = 4 × side) are direct proportion. Age and height change together, but they are neither direct nor inverse proportion.

The correct option is mean 8, median 7, mode 5. The total is 64, so the mean is 64 ÷ 8 = 8. With an even number of values, the median is the average of the middle two (6 and 8), which is 7. The mode is 5, which appears twice. The option with median 6 takes only one of the middle values, the option with mean 7 and median 8 swaps the mean and the median, and the option with mode 15 confuses the mode with the maximum.

The answer is 12. There are 4 choices for chair, and for each, 3 remaining people for vice-chair: 4 × 3 = 12. 6 is the number of ways to pick 2 people without roles. 16 also counts one person holding both posts, and 24 is the number of ways to line up all four people.

The answer is 87. The five tests must total 75 × 5 = 375, and the first four total 72 × 4 = 288, so 375 − 288 = 87. 78 adds the difference of 3 to 75. 75 is just the target mean, and 90 has no basis.

The answer is line graph: Grade 4. A line graph shows change over time. A bar graph (Grade 3) compares amounts by item, a pie chart (Grade 5) shows parts of a whole, and a histogram or other frequency-distribution graph (Grade 6) shows how data are spread. The grades are right, but these graphs do not suit temperature change.